Block #69,770

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/20/2013, 10:22:48 AM · Difficulty 8.9914 · 6,739,950 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eed0d8c39099044886d160c50e4705ebc571fd8d7d0b3964dd7c4e08d5a508ea

View on Chainz ↗

Height

#69,770

Difficulty

8.991355

Transactions

Size

7.51 KB

Version

Bits

08fdc979

Nonce

475

Timestamp

7/20/2013, 10:22:48 AM

Confirmations

6,739,950

Mined by

⛏️ P2SHAJx6m8k1Puo52auktSD3Egy2Nj7Py1oDVs

Merkle Root

8e0b68bca4671fda017164838c98654c9f6e80e2f679ba0cf8815853ffba331a

Transactions (2)

Coinbase8bf559c596c501…7147ff81f64397

1 in → 1 out12.4300 XPM110 B

AJx6m8k1…7Py1oDVs

eedfb64b9caa30…0553be8c5a4a95

65 in → 2 out804.8400 XPM7.31 KB

AdmKVAxM…4D85iGjj ALzoKYZg…eWBka2dD

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.

9.897 × 10¹⁰⁴(105-digit number)

98975175839773471139…28250325032838987619

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

9.897 × 10¹⁰⁴(105-digit number)

98975175839773471139…28250325032838987619

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.897 × 10¹⁰⁴(105-digit number)

98975175839773471139…28250325032838987621

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

1.979 × 10¹⁰⁵(106-digit number)

19795035167954694227…56500650065677975239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.979 × 10¹⁰⁵(106-digit number)

19795035167954694227…56500650065677975241

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

3.959 × 10¹⁰⁵(106-digit number)

39590070335909388455…13001300131355950479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.959 × 10¹⁰⁵(106-digit number)

39590070335909388455…13001300131355950481

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

7.918 × 10¹⁰⁵(106-digit number)

79180140671818776911…26002600262711900959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.918 × 10¹⁰⁵(106-digit number)

79180140671818776911…26002600262711900961

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

1.583 × 10¹⁰⁶(107-digit number)

15836028134363755382…52005200525423801919

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 #69,770

Cookie Preferences