Block #1,244,551

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/20/2015, 8:11:32 AM · Difficulty 10.7446 · 5,569,472 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9fb97953b20fcf4e812a1e681f04931d7fadb0af45be5d4085140d88f6ca8dbc

View on Chainz ↗

Height

#1,244,551

Difficulty

10.744621

Transactions

Size

1.09 KB

Version

Bits

0abe9f7a

Nonce

753,591,221

Timestamp

9/20/2015, 8:11:32 AM

Confirmations

5,569,472

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

496ef5065c07cb183ee5a45b5822f8c3c080b0dd54020d9b6bbac6052c24e1ce

Transactions (5)

Coinbase9a18acfcf89cbf…edd28be4f13c29

1 in → 1 out8.6900 XPM116 B

AJCEY9yy…tg97E6zm

7441124a7bd6d3…1272efde31323a

1 in → 2 out7.5535 XPM227 B

AXd6mZxS…7R3DQLCK AbUxtSrf…pU3EEf4j

e7394ad25f5ac6…3749d81d608cad

1 in → 2 out7.6087 XPM226 B

AU4f4km9…u8UnNcJ8 APGmrDGE…Yk6K9vae

8cee4a1ba5c6cb…d94b2b1f68f48d

1 in → 2 out3.5194 XPM226 B

AGHTMTG1…vWFEswKX AcuM7XiJ…5uND8Jce

69c21fcc603af3…6d54cbf07b8a5b

1 in → 2 out7.1755 XPM227 B

AdTbBadz…tctxCptB AHHmR85y…uEUgHRhd

Prime Chain Origin

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

1.290 × 10⁹⁸(99-digit number)

12909564219812088065…20554619931269695999

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

1.290 × 10⁹⁸(99-digit number)

12909564219812088065…20554619931269695999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.290 × 10⁹⁸(99-digit number)

12909564219812088065…20554619931269696001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

2.581 × 10⁹⁸(99-digit number)

25819128439624176130…41109239862539391999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.581 × 10⁹⁸(99-digit number)

25819128439624176130…41109239862539392001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

5.163 × 10⁹⁸(99-digit number)

51638256879248352260…82218479725078783999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.163 × 10⁹⁸(99-digit number)

51638256879248352260…82218479725078784001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.032 × 10⁹⁹(100-digit number)

10327651375849670452…64436959450157567999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.032 × 10⁹⁹(100-digit number)

10327651375849670452…64436959450157568001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

2.065 × 10⁹⁹(100-digit number)

20655302751699340904…28873918900315135999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.065 × 10⁹⁹(100-digit number)

20655302751699340904…28873918900315136001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #1,244,551

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