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Block #471,684

TWNLength 10ā˜…ā˜…ā˜†ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 4/2/2014, 6:09:09 PM Ā· Difficulty 10.4354 Ā· 6,346,320 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
77f973d5c24a0512480cd127368241885feee6ae13477511878c264405d9b301
View on Chainz ā†—

Height

#471,684

Difficulty

10.435401

Transactions

1

Size

969 B

Version

2

Bits

0a6f7675

Nonce

19,967

Timestamp

4/2/2014, 6:09:09 PM

Confirmations

6,346,320

Mined by

ā›ļø 2aS<SsAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

178ba6bcdae2fae810c60a49d9c8db1f4dc8951f4452409c1717b3dcefa146bc
Transactions (1)
Coinbase178ba6bcdae2faā€¦17b3dcefa146bc
1 in ā†’ 24 out9.1700 XPM879 B
AQvZBsUoā€¦hppgRZTJANNg88pGā€¦ppn21sTeAdxPNkWDā€¦ZMa9u34qAQ8QAT3Jā€¦rCFKuVbRATKK7iFzā€¦wZm46KN1
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.

2.512 Ɨ 10ā¹ā“(95-digit number)
25124912183847677848ā€¦39637141072588145919
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
2.512 Ɨ 10ā¹ā“(95-digit number)
25124912183847677848ā€¦39637141072588145919
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
2.512 Ɨ 10ā¹ā“(95-digit number)
25124912183847677848ā€¦39637141072588145921
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
5.024 Ɨ 10ā¹ā“(95-digit number)
50249824367695355696ā€¦79274282145176291839
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
5.024 Ɨ 10ā¹ā“(95-digit number)
50249824367695355696ā€¦79274282145176291841
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
1.004 Ɨ 10ā¹āµ(96-digit number)
10049964873539071139ā€¦58548564290352583679
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
1.004 Ɨ 10ā¹āµ(96-digit number)
10049964873539071139ā€¦58548564290352583681
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
2.009 Ɨ 10ā¹āµ(96-digit number)
20099929747078142278ā€¦17097128580705167359
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
2.009 Ɨ 10ā¹āµ(96-digit number)
20099929747078142278ā€¦17097128580705167361
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
4.019 Ɨ 10ā¹āµ(96-digit number)
40199859494156284557ā€¦34194257161410334719
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
4.019 Ɨ 10ā¹āµ(96-digit number)
40199859494156284557ā€¦34194257161410334721
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^4 Ɨ origin + 1 āˆ’ 2^4 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,788,097 XPMĀ·at block #6,818,003 Ā· updates every 60s
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