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Block #114,909

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/13/2013, 10:53:58 AM Β· Difficulty 9.7414 Β· 6,686,870 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
08fe3761244c9a4c82486611b8ffdc4d2fdb3120f78f3e342b02a82b0ddf9b48
View on Chainz β†—

Height

#114,909

Difficulty

9.741351

Transactions

1

Size

201 B

Version

2

Bits

09bdc928

Nonce

199,327

Timestamp

8/13/2013, 10:53:58 AM

Confirmations

6,686,870

Mined by

⛏️ P2SHAQLMZDQaC8PMbLa4ZoLenVxqmC26A3Uti1

Merkle Root

fcbade1ecc874770d0ef7a0df23afeec4171b4f09c5b5ed69bfd0f17af1d74ca
Transactions (1)
Coinbasefcbade1ecc8747…fd0f17af1d74ca
1 in β†’ 1 out10.5200 XPM109 B
AQLMZDQa…26A3Uti1
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.

6.338 Γ— 10⁹⁹(100-digit number)
63381453048818009225…48067212890446544959
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
6.338 Γ— 10⁹⁹(100-digit number)
63381453048818009225…48067212890446544959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.338 Γ— 10⁹⁹(100-digit number)
63381453048818009225…48067212890446544961
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
1.267 Γ— 10¹⁰⁰(101-digit number)
12676290609763601845…96134425780893089919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.267 Γ— 10¹⁰⁰(101-digit number)
12676290609763601845…96134425780893089921
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
2.535 Γ— 10¹⁰⁰(101-digit number)
25352581219527203690…92268851561786179839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.535 Γ— 10¹⁰⁰(101-digit number)
25352581219527203690…92268851561786179841
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
5.070 Γ— 10¹⁰⁰(101-digit number)
50705162439054407380…84537703123572359679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.070 Γ— 10¹⁰⁰(101-digit number)
50705162439054407380…84537703123572359681
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
1.014 Γ— 10¹⁰¹(102-digit number)
10141032487810881476…69075406247144719359
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:57,658,319 XPMΒ·at block #6,801,778 Β· updates every 60s
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