Block #119,580

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/16/2013, 2:04:27 PM · Difficulty 9.7499 · 6,695,560 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

94825693db4b6dd20209c58bbf3d80d97b2b350fd832f5ade743e1165abef829

View on Chainz ↗

Height

#119,580

Difficulty

9.749912

Transactions

Size

620 B

Version

Bits

09bffa3e

Nonce

450,527

Timestamp

8/16/2013, 2:04:27 PM

Confirmations

6,695,560

Mined by

⛏️ P2SHAXFB2a1h2CUhX8awGAn712kyRd1hKwNkVm

Merkle Root

ea5d28750155454674e8ccd7053f872c4ea0bf8a246ab8564c6b277429144d78

Transactions (3)

Coinbase46dd5c3703980a…993bad616005b2

1 in → 1 out10.5200 XPM109 B

AXFB2a1h…1hKwNkVm

445a4e1658eaae…bf6552c4c6d780

1 in → 1 out10.5000 XPM158 B

AKN6pNCw…MeATKM2o

ee7eee51c29d46…ac086cda4b05ab

1 in → 3 out67.7833 XPM261 B

APtmyHax…JvhsUh4F AcBv2PMk…FnZkSn2p AUwKMCYC…hHVVSiWv

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.

3.878 × 10⁹⁹(100-digit number)

38783023416211249985…12779731339713704099

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

3.878 × 10⁹⁹(100-digit number)

38783023416211249985…12779731339713704099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.878 × 10⁹⁹(100-digit number)

38783023416211249985…12779731339713704101

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

7.756 × 10⁹⁹(100-digit number)

77566046832422499970…25559462679427408199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.756 × 10⁹⁹(100-digit number)

77566046832422499970…25559462679427408201

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

1.551 × 10¹⁰⁰(101-digit number)

15513209366484499994…51118925358854816399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.551 × 10¹⁰⁰(101-digit number)

15513209366484499994…51118925358854816401

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

3.102 × 10¹⁰⁰(101-digit number)

31026418732968999988…02237850717709632799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.102 × 10¹⁰⁰(101-digit number)

31026418732968999988…02237850717709632801

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

6.205 × 10¹⁰⁰(101-digit number)

62052837465937999976…04475701435419265599

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 #119,580

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