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Block #204,550

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/11/2013, 1:51:37 PM Β· Difficulty 9.8988 Β· 6,603,336 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
435653c8ab603a46bd757123882c06b19a4afcd7caa9e31e04c2b8945dc0f08e
View on Chainz β†—

Height

#204,550

Difficulty

9.898836

Transactions

1

Size

198 B

Version

2

Bits

09e61a16

Nonce

17,520

Timestamp

10/11/2013, 1:51:37 PM

Confirmations

6,603,336

Mined by

⛏️ P2SHASHCgr3FcMvAMVeUbxmte178wGe7VPFbY8

Merkle Root

94819f8a9849ffa460d2a4522922eefd545d9a5ac18b4ede986aa686e8a986e1
Transactions (1)
Coinbase94819f8a9849ff…6aa686e8a986e1
1 in β†’ 1 out10.1900 XPM109 B
ASHCgr3F…e7VPFbY8
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.

1.063 Γ— 10⁹³(94-digit number)
10637092609665962109…34400236255042780799
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
1.063 Γ— 10⁹³(94-digit number)
10637092609665962109…34400236255042780799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.063 Γ— 10⁹³(94-digit number)
10637092609665962109…34400236255042780801
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
2.127 Γ— 10⁹³(94-digit number)
21274185219331924218…68800472510085561599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.127 Γ— 10⁹³(94-digit number)
21274185219331924218…68800472510085561601
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
4.254 Γ— 10⁹³(94-digit number)
42548370438663848437…37600945020171123199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.254 Γ— 10⁹³(94-digit number)
42548370438663848437…37600945020171123201
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
8.509 Γ— 10⁹³(94-digit number)
85096740877327696874…75201890040342246399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.509 Γ— 10⁹³(94-digit number)
85096740877327696874…75201890040342246401
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
1.701 Γ— 10⁹⁴(95-digit number)
17019348175465539374…50403780080684492799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.701 Γ— 10⁹⁴(95-digit number)
17019348175465539374…50403780080684492801
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:57,707,123 XPMΒ·at block #6,807,885 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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