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Block #104,957

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/8/2013, 7:22:14 AM Β· Difficulty 9.5710 Β· 6,699,946 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
13dd684fec79efcb5c9acab4206aed6294a9a36176a94d99163578860be7286c
View on Chainz β†—

Height

#104,957

Difficulty

9.571025

Transactions

1

Size

201 B

Version

2

Bits

09922eb9

Nonce

280,265

Timestamp

8/8/2013, 7:22:14 AM

Confirmations

6,699,946

Mined by

⛏️ P2SHATzEHZ7ayQf8Js5VJS7Me8qrBi2eAGweip

Merkle Root

94f09516109dd2f0ea3e3d676ee6573dcfe13b94f4c995d5174e511be78b8e1e
Transactions (1)
Coinbase94f09516109dd2…4e511be78b8e1e
1 in β†’ 1 out10.9000 XPM109 B
ATzEHZ7a…2eAGweip
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.

2.756 Γ— 10⁹⁸(99-digit number)
27560217693304251933…61387535529829167399
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
2.756 Γ— 10⁹⁸(99-digit number)
27560217693304251933…61387535529829167399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.756 Γ— 10⁹⁸(99-digit number)
27560217693304251933…61387535529829167401
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
5.512 Γ— 10⁹⁸(99-digit number)
55120435386608503867…22775071059658334799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.512 Γ— 10⁹⁸(99-digit number)
55120435386608503867…22775071059658334801
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
1.102 Γ— 10⁹⁹(100-digit number)
11024087077321700773…45550142119316669599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.102 Γ— 10⁹⁹(100-digit number)
11024087077321700773…45550142119316669601
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
2.204 Γ— 10⁹⁹(100-digit number)
22048174154643401547…91100284238633339199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.204 Γ— 10⁹⁹(100-digit number)
22048174154643401547…91100284238633339201
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
4.409 Γ— 10⁹⁹(100-digit number)
44096348309286803094…82200568477266678399
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:57,683,295 XPMΒ·at block #6,804,902 Β· updates every 60s
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