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Block #3,062,574

TWNLength 11ā˜…ā˜…ā˜…ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 2/21/2019, 12:28:53 PM Ā· Difficulty 11.0078 Ā· 3,780,642 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dedf5296dace7206a3dd63dc8cf75abbbd7ee9e9c9c2541df86ea183cfc502f8
View on Chainz ā†—

Height

#3,062,574

Difficulty

11.007826

Transactions

3

Size

765 B

Version

2

Bits

0b0200e1

Nonce

94,732,426

Timestamp

2/21/2019, 12:28:53 PM

Confirmations

3,780,642

Mined by

ā›ļø P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

e1958f95db6a9e5580b29db69628721dd2f1d622d3f29137df0ff4967d09d6b8
Transactions (3)
Coinbase6a173858b31a80ā€¦d1f7ed8c33acc5
1 in ā†’ 1 out8.2600 XPM109 B
AUMQRepmā€¦tAfKmdW1
ef320f59d10d4eā€¦3ea3b1addebf38
2 in ā†’ 2 out11.3942 XPM339 B
AZtM1QsLā€¦JugreUPyAbXwmGxDā€¦4XXYP765
6e95126e917241ā€¦bf853657a84ca1
1 in ā†’ 2 out1.7979 XPM227 B
AbXwmGxDā€¦4XXYP765AP21FpxCā€¦ntAWgp39
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.

9.406 Ɨ 10ā¹ā“(95-digit number)
94062097808893967842ā€¦85087319067387883199
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
9.406 Ɨ 10ā¹ā“(95-digit number)
94062097808893967842ā€¦85087319067387883199
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
9.406 Ɨ 10ā¹ā“(95-digit number)
94062097808893967842ā€¦85087319067387883201
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
1.881 Ɨ 10ā¹āµ(96-digit number)
18812419561778793568ā€¦70174638134775766399
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
1.881 Ɨ 10ā¹āµ(96-digit number)
18812419561778793568ā€¦70174638134775766401
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
3.762 Ɨ 10ā¹āµ(96-digit number)
37624839123557587137ā€¦40349276269551532799
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
3.762 Ɨ 10ā¹āµ(96-digit number)
37624839123557587137ā€¦40349276269551532801
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
7.524 Ɨ 10ā¹āµ(96-digit number)
75249678247115174274ā€¦80698552539103065599
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
7.524 Ɨ 10ā¹āµ(96-digit number)
75249678247115174274ā€¦80698552539103065601
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
1.504 Ɨ 10ā¹ā¶(97-digit number)
15049935649423034854ā€¦61397105078206131199
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
1.504 Ɨ 10ā¹ā¶(97-digit number)
15049935649423034854ā€¦61397105078206131201
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
3.009 Ɨ 10ā¹ā¶(97-digit number)
30099871298846069709ā€¦22794210156412262399
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:57,990,101 XPMĀ·at block #6,843,215 Ā· updates every 60s
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