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Block #207,942

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/13/2013, 5:36:39 PM Β· Difficulty 9.9046 Β· 6,595,824 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3cd9168031e8f19fab6739d662f5f9102598f7457738e366e5304d0c622a526d
View on Chainz β†—

Height

#207,942

Difficulty

9.904628

Transactions

1

Size

197 B

Version

2

Bits

09e795b1

Nonce

164,705

Timestamp

10/13/2013, 5:36:39 PM

Confirmations

6,595,824

Mined by

⛏️ P2SHANcX13Fk7xSX8wFr5zRphRpXHx1biNXNGx

Merkle Root

bc79c50e301474d7fbfe7774245a3ec4159b8fd5d7171898d36e5d878ccbedfd
Transactions (1)
Coinbasebc79c50e301474…6e5d878ccbedfd
1 in β†’ 1 out10.1800 XPM109 B
ANcX13Fk…1biNXNGx
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.

5.860 Γ— 10⁸⁸(89-digit number)
58605062244448980537…58718872059333000219
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
5.860 Γ— 10⁸⁸(89-digit number)
58605062244448980537…58718872059333000219
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.860 Γ— 10⁸⁸(89-digit number)
58605062244448980537…58718872059333000221
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
1.172 Γ— 10⁸⁹(90-digit number)
11721012448889796107…17437744118666000439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.172 Γ— 10⁸⁹(90-digit number)
11721012448889796107…17437744118666000441
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
2.344 Γ— 10⁸⁹(90-digit number)
23442024897779592215…34875488237332000879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.344 Γ— 10⁸⁹(90-digit number)
23442024897779592215…34875488237332000881
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
4.688 Γ— 10⁸⁹(90-digit number)
46884049795559184430…69750976474664001759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.688 Γ— 10⁸⁹(90-digit number)
46884049795559184430…69750976474664001761
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
9.376 Γ— 10⁸⁹(90-digit number)
93768099591118368860…39501952949328003519
Verify on FactorDB β†—Wolfram Alpha β†—

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 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
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 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:57,674,165 XPMΒ·at block #6,803,765 Β· updates every 60s
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