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Block #474,735

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/4/2014, 6:19:25 PM Β· Difficulty 10.4555 Β· 6,367,562 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9521289565974ab09626082f346bc08c2ce7a6f8218b1b4cee00fb482e8de274
View on Chainz β†—

Height

#474,735

Difficulty

10.455537

Transactions

1

Size

203 B

Version

2

Bits

0a749e17

Nonce

24,239

Timestamp

4/4/2014, 6:19:25 PM

Confirmations

6,367,562

Mined by

⛏️ P2SHAMEm9DTFoTkmfvfCrYw9q81LrVNXQcZ89p

Merkle Root

d1e6829b6ed7ddd70a1be995537e5f480629f338a44bf0e1fabf51222efc6409
Transactions (1)
Coinbased1e6829b6ed7dd…bf51222efc6409
1 in β†’ 1 out9.1300 XPM112 B
AMEm9DTF…NXQcZ89p
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.518 Γ— 10⁹⁸(99-digit number)
15184260120635800764…79705643703389168639
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.518 Γ— 10⁹⁸(99-digit number)
15184260120635800764…79705643703389168639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.518 Γ— 10⁹⁸(99-digit number)
15184260120635800764…79705643703389168641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
3.036 Γ— 10⁹⁸(99-digit number)
30368520241271601528…59411287406778337279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.036 Γ— 10⁹⁸(99-digit number)
30368520241271601528…59411287406778337281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
6.073 Γ— 10⁹⁸(99-digit number)
60737040482543203056…18822574813556674559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.073 Γ— 10⁹⁸(99-digit number)
60737040482543203056…18822574813556674561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.214 Γ— 10⁹⁹(100-digit number)
12147408096508640611…37645149627113349119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.214 Γ— 10⁹⁹(100-digit number)
12147408096508640611…37645149627113349121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.429 Γ— 10⁹⁹(100-digit number)
24294816193017281222…75290299254226698239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.429 Γ— 10⁹⁹(100-digit number)
24294816193017281222…75290299254226698241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,982,780 XPMΒ·at block #6,842,296 Β· updates every 60s
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