Block #461,509

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/26/2014, 6:53:48 PM · Difficulty 10.4152 · 6,345,109 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

613bbb1b92720aff4f5bfd5375599767974782f23befe4426831d3a82733e6b7

View on Chainz ↗

Height

#461,509

Difficulty

10.415217

Transactions

Size

1.08 KB

Version

Bits

0a6a4ba4

Nonce

54,555,425

Timestamp

3/26/2014, 6:53:48 PM

Confirmations

6,345,109

Mined by

⛏️ P2SHAHymEiG6yjjiqz7kJv9HBd6mMUtfnBVmtm

Merkle Root

15e6eb0b3af68cd13691b08e0226aabbd49d727a75f2a8584081fca46999658e

Transactions (5)

Coinbase2c92291dc2fb29…a5854a00f2bfa1

1 in → 1 out9.2400 XPM109 B

AHymEiG6…tfnBVmtm

75573a9671e533…c3a75d93e521ba

1 in → 2 out8.1658 XPM225 B

AXVqL4KM…bJPeTWdV AYUSgd4j…jwoYX7K3

2de926c1e1a345…1da182e26c6d07

1 in → 2 out8.1648 XPM225 B

AaTa1TJW…CS1ZqFKG AVHf94me…fvWm1PqL

9273acdc25817c…d6078de04bbc7c

1 in → 2 out8.1682 XPM226 B

AYrLXeP4…p3kp1osZ AT36kbgB…xrZ2aLYw

80cb07c1d6f2b3…9fc723c0fc3ad1

1 in → 2 out8.1657 XPM226 B

AWy6kpsx…m7f6kmrX APCza2xF…NYW1bK7F

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.

8.087 × 10⁹⁶(97-digit number)

80871016057695856765…43100101832376703999

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

8.087 × 10⁹⁶(97-digit number)

80871016057695856765…43100101832376703999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.087 × 10⁹⁶(97-digit number)

80871016057695856765…43100101832376704001

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

1.617 × 10⁹⁷(98-digit number)

16174203211539171353…86200203664753407999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.617 × 10⁹⁷(98-digit number)

16174203211539171353…86200203664753408001

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

3.234 × 10⁹⁷(98-digit number)

32348406423078342706…72400407329506815999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.234 × 10⁹⁷(98-digit number)

32348406423078342706…72400407329506816001

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

6.469 × 10⁹⁷(98-digit number)

64696812846156685412…44800814659013631999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.469 × 10⁹⁷(98-digit number)

64696812846156685412…44800814659013632001

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

1.293 × 10⁹⁸(99-digit number)

12939362569231337082…89601629318027263999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.293 × 10⁹⁸(99-digit number)

12939362569231337082…89601629318027264001

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 #461,509

Cookie Preferences