Block #569,968

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/31/2014, 12:27:03 PM · Difficulty 10.9648 · 6,225,419 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0b953dc9423d693dcb641585c775afbbb42818a000d993847bad6b6e6f467946

View on Chainz ↗

Height

#569,968

Difficulty

10.964751

Transactions

Size

922 B

Version

Bits

0af6f9f0

Nonce

62,360,867

Timestamp

5/31/2014, 12:27:03 PM

Confirmations

6,225,419

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

6b194f92ac0fa52c135b299d2a07ce171246e95344fa3002e966f72a60df6f1c

Transactions (3)

Coinbase902b4324ae7ce6…6ea10bce4cd808

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

c04f7c4b083c40…12f36bf77c9435

1 in → 1 out18.1400 XPM192 B

AbJsVHpT…rsAXatcN

f99b71e2ca3593…5e59ecf829d3db

3 in → 2 out7.8056 XPM522 B

AdJyG9sn…T5qbrRs8 ASEkR768…35s3LmSu

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.

2.534 × 10¹⁰⁰(101-digit number)

25349639149668244013…29195741475045990399

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

2.534 × 10¹⁰⁰(101-digit number)

25349639149668244013…29195741475045990399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.534 × 10¹⁰⁰(101-digit number)

25349639149668244013…29195741475045990401

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

5.069 × 10¹⁰⁰(101-digit number)

50699278299336488026…58391482950091980799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.069 × 10¹⁰⁰(101-digit number)

50699278299336488026…58391482950091980801

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

1.013 × 10¹⁰¹(102-digit number)

10139855659867297605…16782965900183961599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.013 × 10¹⁰¹(102-digit number)

10139855659867297605…16782965900183961601

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

2.027 × 10¹⁰¹(102-digit number)

20279711319734595210…33565931800367923199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.027 × 10¹⁰¹(102-digit number)

20279711319734595210…33565931800367923201

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

4.055 × 10¹⁰¹(102-digit number)

40559422639469190421…67131863600735846399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.055 × 10¹⁰¹(102-digit number)

40559422639469190421…67131863600735846401

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

8.111 × 10¹⁰¹(102-digit number)

81118845278938380842…34263727201471692799

Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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

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 × 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