Block #274,538

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 8:13:44 AM · Difficulty 9.9578 · 6,523,258 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1fd8d1954620c99ead96a4b1693cf175be813670d11d3e452e7ed3dbdd1b600d

View on Chainz ↗

Height

#274,538

Difficulty

9.957790

Transactions

Size

863 B

Version

Bits

09f531b8

Nonce

116,429

Timestamp

11/26/2013, 8:13:44 AM

Confirmations

6,523,258

Mined by

⛏️ j0aRX!AYSTY5gDRsT8n1RJteYKydyLA7my21Gwsc

Merkle Root

428d3e9759223e643ee6860bd9aa1562c055bbc0737a745acae7af2e92dc6e8a

Transactions (4)

Coinbase124f73dfb7bc2a…dba3b925505c11

1 in → 1 out10.0700 XPM97 B

AYSTY5gD…my21Gwsc

f2b6ea1f895861…734050422f207e

1 in → 2 out10.2562 XPM227 B

AXp3nw5U…7qHpfHLU APjj6kRY…y6fnQt24

30aff3fdce0c8e…72e09288af9050

1 in → 2 out6.0058 XPM225 B

AGxb8X2h…ERKAnTCc AKNcXTKQ…C5ScyiL4

4a4ebf3f6f2914…2dbcceb3816063

1 in → 2 out8.0509 XPM226 B

AadgHu7f…VfBrCE88 AMudz6Nm…7TzCLLZg

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.

1.067 × 10⁹¹(92-digit number)

10671258146197602320…02814205590449285999

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

1.067 × 10⁹¹(92-digit number)

10671258146197602320…02814205590449285999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.067 × 10⁹¹(92-digit number)

10671258146197602320…02814205590449286001

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

2.134 × 10⁹¹(92-digit number)

21342516292395204641…05628411180898571999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.134 × 10⁹¹(92-digit number)

21342516292395204641…05628411180898572001

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

4.268 × 10⁹¹(92-digit number)

42685032584790409283…11256822361797143999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.268 × 10⁹¹(92-digit number)

42685032584790409283…11256822361797144001

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

8.537 × 10⁹¹(92-digit number)

85370065169580818566…22513644723594287999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.537 × 10⁹¹(92-digit number)

85370065169580818566…22513644723594288001

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

1.707 × 10⁹²(93-digit number)

17074013033916163713…45027289447188575999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.707 × 10⁹²(93-digit number)

17074013033916163713…45027289447188576001

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