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Block #375,370

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/25/2014, 4:16:45 PM Β· Difficulty 10.4235 Β· 6,430,602 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
343d6e143e0add37df5c6cee0e32b0d9eeb9d6444d2d188e4e4f81197b7d5741
View on Chainz β†—

Height

#375,370

Difficulty

10.423529

Transactions

1

Size

231 B

Version

2

Bits

0a6c6c68

Nonce

1,303

Timestamp

1/25/2014, 4:16:45 PM

Confirmations

6,430,602

Mined by

⛏️ P2SHAN9iEquXMLkQ4kBwmAbtH5ubSEJ6V8wYsN

Merkle Root

08e113e3a48c406440eda760aef96223091cbe7879b4196fe42e0c1efda32879
Transactions (1)
Coinbase08e113e3a48c40…2e0c1efda32879
1 in β†’ 2 out9.1900 XPM137 B
AN9iEquX…J6V8wYsNAbiw8n3q…ZnZfgvQW
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.

5.016 Γ— 10¹⁰³(104-digit number)
50169732991752897064…24287261690685174559
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
5.016 Γ— 10¹⁰³(104-digit number)
50169732991752897064…24287261690685174559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.016 Γ— 10¹⁰³(104-digit number)
50169732991752897064…24287261690685174561
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
1.003 Γ— 10¹⁰⁴(105-digit number)
10033946598350579412…48574523381370349119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.003 Γ— 10¹⁰⁴(105-digit number)
10033946598350579412…48574523381370349121
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
2.006 Γ— 10¹⁰⁴(105-digit number)
20067893196701158825…97149046762740698239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.006 Γ— 10¹⁰⁴(105-digit number)
20067893196701158825…97149046762740698241
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
4.013 Γ— 10¹⁰⁴(105-digit number)
40135786393402317651…94298093525481396479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.013 Γ— 10¹⁰⁴(105-digit number)
40135786393402317651…94298093525481396481
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
8.027 Γ— 10¹⁰⁴(105-digit number)
80271572786804635303…88596187050962792959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.027 Γ— 10¹⁰⁴(105-digit number)
80271572786804635303…88596187050962792961
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:57,691,851 XPMΒ·at block #6,805,971 Β· updates every 60s
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