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Block #78,408

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/22/2013, 7:46:54 PM Β· Difficulty 9.2346 Β· 6,725,121 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a0377383efc296049edb29ed2735a093bd8bc8693dd4670b07bfda3e4ec4167d
View on Chainz β†—

Height

#78,408

Difficulty

9.234631

Transactions

1

Size

202 B

Version

2

Bits

093c10cd

Nonce

355

Timestamp

7/22/2013, 7:46:54 PM

Confirmations

6,725,121

Mined by

⛏️ P2SHASvAfAKFRXtJK74VVq8AGFHHRvVJ38GfHD

Merkle Root

050e716ae724508446604dcc4b261592b1a2bbe2946392db769f363add56cd74
Transactions (1)
Coinbase050e716ae72450…9f363add56cd74
1 in β†’ 1 out11.7100 XPM110 B
ASvAfAKF…VJ38GfHD
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.

2.506 Γ— 10⁹⁹(100-digit number)
25068169114556970272…43989573872407088519
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
2.506 Γ— 10⁹⁹(100-digit number)
25068169114556970272…43989573872407088519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.506 Γ— 10⁹⁹(100-digit number)
25068169114556970272…43989573872407088521
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
5.013 Γ— 10⁹⁹(100-digit number)
50136338229113940545…87979147744814177039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.013 Γ— 10⁹⁹(100-digit number)
50136338229113940545…87979147744814177041
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
1.002 Γ— 10¹⁰⁰(101-digit number)
10027267645822788109…75958295489628354079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.002 Γ— 10¹⁰⁰(101-digit number)
10027267645822788109…75958295489628354081
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
2.005 Γ— 10¹⁰⁰(101-digit number)
20054535291645576218…51916590979256708159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.005 Γ— 10¹⁰⁰(101-digit number)
20054535291645576218…51916590979256708161
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
4.010 Γ— 10¹⁰⁰(101-digit number)
40109070583291152436…03833181958513416319
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:57,672,260 XPMΒ·at block #6,803,528 Β· updates every 60s
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