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Block #111,803

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/11/2013, 3:38:36 PM Β· Difficulty 9.7136 Β· 6,699,116 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fb6757476aba44b422bf6cd8dc287143624d1fc447abf65ba3cb7d6d84e49e5a
View on Chainz β†—

Height

#111,803

Difficulty

9.713568

Transactions

1

Size

201 B

Version

2

Bits

09b6ac64

Nonce

166,672

Timestamp

8/11/2013, 3:38:36 PM

Confirmations

6,699,116

Mined by

⛏️ P2SHAVN5TcQu993EfviCkpQSYHiBxtuDJ9ZxKG

Merkle Root

ec8333ceac1697e6fd096a1fa2e85be1d308195c4b7515d21ad4b86dcb690336
Transactions (1)
Coinbaseec8333ceac1697…d4b86dcb690336
1 in β†’ 1 out10.5800 XPM109 B
AVN5TcQu…uDJ9ZxKG
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.

1.242 Γ— 10¹⁰⁰(101-digit number)
12426584573433065783…15107158413465271599
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
1.242 Γ— 10¹⁰⁰(101-digit number)
12426584573433065783…15107158413465271599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.242 Γ— 10¹⁰⁰(101-digit number)
12426584573433065783…15107158413465271601
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
2.485 Γ— 10¹⁰⁰(101-digit number)
24853169146866131567…30214316826930543199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.485 Γ— 10¹⁰⁰(101-digit number)
24853169146866131567…30214316826930543201
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
4.970 Γ— 10¹⁰⁰(101-digit number)
49706338293732263135…60428633653861086399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.970 Γ— 10¹⁰⁰(101-digit number)
49706338293732263135…60428633653861086401
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
9.941 Γ— 10¹⁰⁰(101-digit number)
99412676587464526271…20857267307722172799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.941 Γ— 10¹⁰⁰(101-digit number)
99412676587464526271…20857267307722172801
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
1.988 Γ— 10¹⁰¹(102-digit number)
19882535317492905254…41714534615444345599
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:57,731,453 XPMΒ·at block #6,810,918 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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