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Block #464,046

TWNLength 11ā˜…ā˜…ā˜…ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 3/28/2014, 1:04:42 PM Ā· Difficulty 10.4171 Ā· 6,344,835 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a8e1d9055f5e392641072b0dca8ecc03e04291f8f59147bfb4ac1af95822574e
View on Chainz ā†—

Height

#464,046

Difficulty

10.417090

Transactions

3

Size

651 B

Version

2

Bits

0a6ac668

Nonce

31,055,493

Timestamp

3/28/2014, 1:04:42 PM

Confirmations

6,344,835

Mined by

ā›ļø P2SHAGNRqpszwisrUNPciX9dumtme5wj7mMXZA

Merkle Root

cf2d8e63384943023596b21c3057e71c36053fdafe2ba1546341d1851d87aab0
Transactions (3)
Coinbase71c3621fb56cbbā€¦b9657a2ad2e5d4
1 in ā†’ 1 out9.2200 XPM109 B
AGNRqpszā€¦wj7mMXZA
400f8a1f1fbeefā€¦fe3ab865930b89
1 in ā†’ 2 out5.0658 XPM226 B
AYXRZ17Vā€¦V8mgGNNoAHY6nCMxā€¦j2SwA5M2
a3aabe685be6d6ā€¦9bef13391c9a36
1 in ā†’ 2 out1.0687 XPM226 B
AYosxsXXā€¦kYVMehY3AUQYhAmBā€¦noBQM9Va
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.

3.825 Ɨ 10ā¹ā“(95-digit number)
38256637822192928795ā€¦77012797873558655399
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
3.825 Ɨ 10ā¹ā“(95-digit number)
38256637822192928795ā€¦77012797873558655399
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
3.825 Ɨ 10ā¹ā“(95-digit number)
38256637822192928795ā€¦77012797873558655401
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
7.651 Ɨ 10ā¹ā“(95-digit number)
76513275644385857590ā€¦54025595747117310799
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
7.651 Ɨ 10ā¹ā“(95-digit number)
76513275644385857590ā€¦54025595747117310801
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
1.530 Ɨ 10ā¹āµ(96-digit number)
15302655128877171518ā€¦08051191494234621599
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
1.530 Ɨ 10ā¹āµ(96-digit number)
15302655128877171518ā€¦08051191494234621601
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
3.060 Ɨ 10ā¹āµ(96-digit number)
30605310257754343036ā€¦16102382988469243199
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
3.060 Ɨ 10ā¹āµ(96-digit number)
30605310257754343036ā€¦16102382988469243201
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
6.121 Ɨ 10ā¹āµ(96-digit number)
61210620515508686072ā€¦32204765976938486399
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
6.121 Ɨ 10ā¹āµ(96-digit number)
61210620515508686072ā€¦32204765976938486401
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
1.224 Ɨ 10ā¹ā¶(97-digit number)
12242124103101737214ā€¦64409531953876972799
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:57,715,100 XPMĀ·at block #6,808,880 Ā· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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