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Block #107,975

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/9/2013, 7:17:27 PM Β· Difficulty 9.6388 Β· 6,697,377 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f8a85b10d4d31926e7428bd5fbcefabb4c8e4f037a047d08671fe4e9076f7b35
View on Chainz β†—

Height

#107,975

Difficulty

9.638801

Transactions

1

Size

200 B

Version

2

Bits

09a3887e

Nonce

100,419

Timestamp

8/9/2013, 7:17:27 PM

Confirmations

6,697,377

Mined by

⛏️ P2SHAZ29sR79QusQVNF36wMX1odggdnKVqwKGr

Merkle Root

d1f97ccdef102dafc8da8b75e1850aaae2d4707b4a44129dd82f832536ddd23e
Transactions (1)
Coinbased1f97ccdef102d…2f832536ddd23e
1 in β†’ 1 out10.7500 XPM109 B
AZ29sR79…nKVqwKGr
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.

1.157 Γ— 10⁹⁸(99-digit number)
11578253451149467884…95522926944199414299
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
1.157 Γ— 10⁹⁸(99-digit number)
11578253451149467884…95522926944199414299
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.157 Γ— 10⁹⁸(99-digit number)
11578253451149467884…95522926944199414301
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
2.315 Γ— 10⁹⁸(99-digit number)
23156506902298935769…91045853888398828599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.315 Γ— 10⁹⁸(99-digit number)
23156506902298935769…91045853888398828601
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
4.631 Γ— 10⁹⁸(99-digit number)
46313013804597871539…82091707776797657199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.631 Γ— 10⁹⁸(99-digit number)
46313013804597871539…82091707776797657201
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
9.262 Γ— 10⁹⁸(99-digit number)
92626027609195743078…64183415553595314399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.262 Γ— 10⁹⁸(99-digit number)
92626027609195743078…64183415553595314401
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
1.852 Γ— 10⁹⁹(100-digit number)
18525205521839148615…28366831107190628799
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:57,686,899 XPMΒ·at block #6,805,351 Β· updates every 60s
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