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Block #2,631,652

TWNLength 11ā˜…ā˜…ā˜…ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 4/27/2018, 6:45:12 AM Ā· Difficulty 11.1744 Ā· 4,211,560 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
9db4539b36332bee1e77c19d57b2df9bd43a4568cac09f8bb9e3be7ce16ef3e7
View on Chainz ā†—

Height

#2,631,652

Difficulty

11.174408

Transactions

4

Size

1.01 KB

Version

2

Bits

0b2ca609

Nonce

187,112,988

Timestamp

4/27/2018, 6:45:12 AM

Confirmations

4,211,560

Mined by

ā›ļø P2SHAYx3Dhs3zm8QsGAj9c3oN4GA9bhKbGDKoF

Merkle Root

ba3648a96f46ae18f163a7af3d37b8821859d43c09e819dbc6c35227a30bf507
Transactions (4)
Coinbase24ac7e50de2225ā€¦7c31e296be63c5
1 in ā†’ 1 out8.0300 XPM109 B
AYx3Dhs3ā€¦hKbGDKoF
5b8cd6dadee26aā€¦b25e34b5f8bec5
3 in ā†’ 2 out23.8600 XPM421 B
AVvgHwJrā€¦kj4GjujcAZNx8JFmā€¦dvnd3xXu
fcaa9b85ed35b9ā€¦6cb258766f33ca
1 in ā†’ 2 out7.9400 XPM192 B
AamnkX56ā€¦Dk9c6QCrAVpcA1Huā€¦nQnBqXTX
a80ef4973fee87ā€¦603acdffe6e48e
1 in ā†’ 2 out2.7740 XPM227 B
ANwtSRNcā€¦za9KnLoDAS8fNJjUā€¦1QViuCQV
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) ā€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.017 Ɨ 10ā¹ā“(95-digit number)
30176327084170039196ā€¦40874649305462320159
Discovered Prime Numbers
Lower: 2^k Ɨ origin āˆ’ 1 | Upper: 2^k Ɨ origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 ā€” Twin Prime Pair (origin Ā± 1)
origin āˆ’ 1
3.017 Ɨ 10ā¹ā“(95-digit number)
30176327084170039196ā€¦40874649305462320159
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
3.017 Ɨ 10ā¹ā“(95-digit number)
30176327084170039196ā€¦40874649305462320161
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: origin + 1 āˆ’ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 1 ā€” Twin Prime Pair (2^1 Ɨ origin Ā± 1)
2^1 Ɨ origin āˆ’ 1
6.035 Ɨ 10ā¹ā“(95-digit number)
60352654168340078393ā€¦81749298610924640319
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
6.035 Ɨ 10ā¹ā“(95-digit number)
60352654168340078393ā€¦81749298610924640321
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^1 Ɨ origin + 1 āˆ’ 2^1 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 2 ā€” Twin Prime Pair (2^2 Ɨ origin Ā± 1)
2^2 Ɨ origin āˆ’ 1
1.207 Ɨ 10ā¹āµ(96-digit number)
12070530833668015678ā€¦63498597221849280639
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
1.207 Ɨ 10ā¹āµ(96-digit number)
12070530833668015678ā€¦63498597221849280641
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^2 Ɨ origin + 1 āˆ’ 2^2 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 3 ā€” Twin Prime Pair (2^3 Ɨ origin Ā± 1)
2^3 Ɨ origin āˆ’ 1
2.414 Ɨ 10ā¹āµ(96-digit number)
24141061667336031357ā€¦26997194443698561279
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
2.414 Ɨ 10ā¹āµ(96-digit number)
24141061667336031357ā€¦26997194443698561281
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^3 Ɨ origin + 1 āˆ’ 2^3 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 4 ā€” Twin Prime Pair (2^4 Ɨ origin Ā± 1)
2^4 Ɨ origin āˆ’ 1
4.828 Ɨ 10ā¹āµ(96-digit number)
48282123334672062714ā€¦53994388887397122559
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
4.828 Ɨ 10ā¹āµ(96-digit number)
48282123334672062714ā€¦53994388887397122561
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^4 Ɨ origin + 1 āˆ’ 2^4 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 5 ā€” Twin Prime Pair (2^5 Ɨ origin Ā± 1)
2^5 Ɨ origin āˆ’ 1
9.656 Ɨ 10ā¹āµ(96-digit number)
96564246669344125429ā€¦07988777774794245119
Verify on FactorDB ā†—Wolfram Alpha ā†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin ā€” the large number shown above ā€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

ā˜…ā˜…ā˜…ā˜†ā˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Ɨ 3 Ɨ 5 Ɨ 7 Ɨ ā€¦), the result is the first prime in the chain. The origin is deliberately divisible by this primorial ā€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Ɨ Primorial (2Ā·3Ā·5Ā·7Ā·11Ā·ā€¦)
Source: Primecoin prime.cpp ā€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors ā€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial āˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,990,069 XPMĀ·at block #6,843,211 Ā· updates every 60s
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