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Block #88,984

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/30/2013, 1:05:11 AM Β· Difficulty 9.2616 Β· 6,705,599 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dcf7ad59f92cb3d8750c71eb354d4f3d9acdef4a7a04860612a5249bf9f0d3f2
View on Chainz β†—

Height

#88,984

Difficulty

9.261614

Transactions

1

Size

205 B

Version

2

Bits

0942f926

Nonce

82,460

Timestamp

7/30/2013, 1:05:11 AM

Confirmations

6,705,599

Mined by

⛏️ P2SHATzEHZ7ayQf8Js5VJS7Me8qrBi2eAGweip

Merkle Root

3306620129faf90ec8ef01f4aec1357c5c668487cc2a0545c374c89da893cc41
Transactions (1)
Coinbase3306620129faf9…74c89da893cc41
1 in β†’ 1 out11.6400 XPM109 B
ATzEHZ7a…2eAGweip
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.

1.247 Γ— 10¹⁰⁹(110-digit number)
12471977124261648226…00602488343906417299
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
1.247 Γ— 10¹⁰⁹(110-digit number)
12471977124261648226…00602488343906417299
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.247 Γ— 10¹⁰⁹(110-digit number)
12471977124261648226…00602488343906417301
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
2.494 Γ— 10¹⁰⁹(110-digit number)
24943954248523296453…01204976687812834599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.494 Γ— 10¹⁰⁹(110-digit number)
24943954248523296453…01204976687812834601
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
4.988 Γ— 10¹⁰⁹(110-digit number)
49887908497046592906…02409953375625669199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.988 Γ— 10¹⁰⁹(110-digit number)
49887908497046592906…02409953375625669201
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
9.977 Γ— 10¹⁰⁹(110-digit number)
99775816994093185813…04819906751251338399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.977 Γ— 10¹⁰⁹(110-digit number)
99775816994093185813…04819906751251338401
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
1.995 Γ— 10¹¹⁰(111-digit number)
19955163398818637162…09639813502502676799
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:57,600,711 XPMΒ·at block #6,794,582 Β· updates every 60s
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