Block #269,430

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/23/2013, 3:32:32 AM · Difficulty 9.9532 · 6,522,482 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2e71925b07fec60ac83ef1925a031a64510729fc1fea250642bba0a4c8423eab

View on Chainz ↗

Height

#269,430

Difficulty

9.953177

Transactions

Size

1.91 KB

Version

Bits

09f40364

Nonce

392,122

Timestamp

11/23/2013, 3:32:32 AM

Confirmations

6,522,482

Merkle Root

001082955db7b0ba2344ea741c26575f8d3b201cc5270c5e7050996ea267e6ca

Transactions (5)

Coinbase51f3e40da1ec4a…d629baa22d71f0

1 in → 1 out10.1200 XPM109 B

AdYjVGXB…nyJ6jiej

c3deb8737625d0…76d05d1495eeb3

2 in → 2 out4.0159 XPM372 B

AZ8JxGHj…j89Lkm34 APaqDLwf…4aXLnDUP

451991d52711b9…98a3dbb743df2a

5 in → 1 out0.5875 XPM783 B

AakCBgDN…KJzYPxJe

56b11437c04dbf…eb5fce750e21d4

1 in → 2 out8.0290 XPM226 B

AJuBQihW…xn2vAFiQ AGBHoTTo…NdDged3x

301ec3b73b6b67…fbd27aaad8ae7e

2 in → 2 out5.6677 XPM374 B

AbiELTnP…1RTRWH9C Ac3x9rqs…3xYmWHz5

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.

3.427 × 10⁹²(93-digit number)

34272802933403857181…56014046378285792359

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

3.427 × 10⁹²(93-digit number)

34272802933403857181…56014046378285792359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.427 × 10⁹²(93-digit number)

34272802933403857181…56014046378285792361

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

6.854 × 10⁹²(93-digit number)

68545605866807714362…12028092756571584719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.854 × 10⁹²(93-digit number)

68545605866807714362…12028092756571584721

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

1.370 × 10⁹³(94-digit number)

13709121173361542872…24056185513143169439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.370 × 10⁹³(94-digit number)

13709121173361542872…24056185513143169441

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

2.741 × 10⁹³(94-digit number)

27418242346723085744…48112371026286338879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.741 × 10⁹³(94-digit number)

27418242346723085744…48112371026286338881

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

5.483 × 10⁹³(94-digit number)

54836484693446171489…96224742052572677759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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