Block #122,786

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/18/2013, 4:53:32 PM · Difficulty 9.7576 · 6,704,521 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

613c74ad58e55ae7d890362bbbbcdb463d1b9423881f301f6ebbb44c62409ea1

View on Chainz ↗

Height

#122,786

Difficulty

9.757642

Transactions

Size

1.15 KB

Version

Bits

09c1f4d9

Nonce

266,207

Timestamp

8/18/2013, 4:53:32 PM

Confirmations

6,704,521

Mined by

⛏️ P2SHAbM5wYqpSUGnF3RggdpUk69Pt3e2ub7k5S

Merkle Root

9396f2055fba2e4b359734dca543cfd9f1d8a296a33f4ea5b7ba7ceb96b808b4

Transactions (3)

Coinbase0167873db93249…85da26f70b6811

1 in → 1 out10.5100 XPM109 B

AbM5wYqp…e2ub7k5S

e7df130bf725ff…9f1d0fbc05ebae

1 in → 2 out10.4900 XPM193 B

AYzeg3S2…k2Cwt8d1 Aca1dndv…g4azZy2F

a6fda0e840a55f…23490c3419e4f6

5 in → 1 out18.5000 XPM783 B

AWUEKpDQ…ceTLLhCD

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.

1.395 × 10⁹⁶(97-digit number)

13959695158684454052…03960388106992084499

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

1.395 × 10⁹⁶(97-digit number)

13959695158684454052…03960388106992084499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.395 × 10⁹⁶(97-digit number)

13959695158684454052…03960388106992084501

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

2.791 × 10⁹⁶(97-digit number)

27919390317368908104…07920776213984168999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.791 × 10⁹⁶(97-digit number)

27919390317368908104…07920776213984169001

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

5.583 × 10⁹⁶(97-digit number)

55838780634737816208…15841552427968337999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.583 × 10⁹⁶(97-digit number)

55838780634737816208…15841552427968338001

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

1.116 × 10⁹⁷(98-digit number)

11167756126947563241…31683104855936675999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.116 × 10⁹⁷(98-digit number)

11167756126947563241…31683104855936676001

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

2.233 × 10⁹⁷(98-digit number)

22335512253895126483…63366209711873351999

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

Block #122,786

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