Block #477,989

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/6/2014, 7:18:25 PM · Difficulty 10.4895 · 6,349,057 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d085913e905f110159380d85a455ea9998b5ba0ab66e1dc8ac829d95d1502aec

View on Chainz ↗

Height

#477,989

Difficulty

10.489475

Transactions

Size

1.73 KB

Version

Bits

0a7d4e44

Nonce

14,303

Timestamp

4/6/2014, 7:18:25 PM

Confirmations

6,349,057

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

6f3fddf7a76cae091c2078d3b598526d00a9e5938ef247865869f25d0613fc25

Transactions (4)

Coinbase548a1df3b1452f…e030fcff1620ac

1 in → 1 out9.1000 XPM116 B

AbwWkWZt…kawDhufa

a44c8f13964564…c07cedd04f8e81

6 in → 2 out54.5964 XPM968 B

ATvTbEFw…eedy57pt AbNM8JvG…zboEKNub

380aab8bdb74fc…e79c8c5751056b

2 in → 2 out17.4066 XPM374 B

AFv6FpGB…HKczmteY AWpGbR2X…k82Qpk4B

826a98e8012bfa…bd5581bec9e795

1 in → 2 out8.1102 XPM226 B

AaGqyCJY…uwrwiKPS AKzfNFxj…QRt3qTfB

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.

6.427 × 10⁹⁷(98-digit number)

64274843432414005524…52255014221133188499

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

6.427 × 10⁹⁷(98-digit number)

64274843432414005524…52255014221133188499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.427 × 10⁹⁷(98-digit number)

64274843432414005524…52255014221133188501

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

1.285 × 10⁹⁸(99-digit number)

12854968686482801104…04510028442266376999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.285 × 10⁹⁸(99-digit number)

12854968686482801104…04510028442266377001

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

2.570 × 10⁹⁸(99-digit number)

25709937372965602209…09020056884532753999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.570 × 10⁹⁸(99-digit number)

25709937372965602209…09020056884532754001

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

5.141 × 10⁹⁸(99-digit number)

51419874745931204419…18040113769065507999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.141 × 10⁹⁸(99-digit number)

51419874745931204419…18040113769065508001

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

1.028 × 10⁹⁹(100-digit number)

10283974949186240883…36080227538131015999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.028 × 10⁹⁹(100-digit number)

10283974949186240883…36080227538131016001

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 #477,989

Cookie Preferences