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Block #108,998

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/10/2013, 6:45:31 AM Β· Difficulty 9.6620 Β· 6,694,630 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c10891174476f77b40f8aec6749683e5c1cb764da2d6f3527472a7655f6b0119
View on Chainz β†—

Height

#108,998

Difficulty

9.662034

Transactions

1

Size

201 B

Version

2

Bits

09a97b16

Nonce

87,883

Timestamp

8/10/2013, 6:45:31 AM

Confirmations

6,694,630

Mined by

⛏️ P2SHAJwT4t7mqNZ7nwyuBKJTxL3n2nrXZrFS9k

Merkle Root

94924bc6f3b36e26a32aaa3ef9db6eb82769ece9970ee6bfdb1c89b7b0dc484c
Transactions (1)
Coinbase94924bc6f3b36e…1c89b7b0dc484c
1 in β†’ 1 out10.7000 XPM109 B
AJwT4t7m…rXZrFS9k
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.

2.878 Γ— 10⁹⁸(99-digit number)
28787423354233181777…16584302544439811499
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
2.878 Γ— 10⁹⁸(99-digit number)
28787423354233181777…16584302544439811499
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.878 Γ— 10⁹⁸(99-digit number)
28787423354233181777…16584302544439811501
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
5.757 Γ— 10⁹⁸(99-digit number)
57574846708466363554…33168605088879622999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.757 Γ— 10⁹⁸(99-digit number)
57574846708466363554…33168605088879623001
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
1.151 Γ— 10⁹⁹(100-digit number)
11514969341693272710…66337210177759245999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.151 Γ— 10⁹⁹(100-digit number)
11514969341693272710…66337210177759246001
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
2.302 Γ— 10⁹⁹(100-digit number)
23029938683386545421…32674420355518491999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.302 Γ— 10⁹⁹(100-digit number)
23029938683386545421…32674420355518492001
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
4.605 Γ— 10⁹⁹(100-digit number)
46059877366773090843…65348840711036983999
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:57,673,056 XPMΒ·at block #6,803,627 Β· updates every 60s
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