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Block #97,189

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/4/2013, 2:21:41 PM Β· Difficulty 9.2965 Β· 6,698,437 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0d3c4a218bf94b13d290c717e5bdc1aeecd2048b52f5212aa0446636abd6c5cb
View on Chainz β†—

Height

#97,189

Difficulty

9.296529

Transactions

1

Size

204 B

Version

2

Bits

094be958

Nonce

2,783

Timestamp

8/4/2013, 2:21:41 PM

Confirmations

6,698,437

Mined by

⛏️ P2SHAFv3H3KXSay9488PtLWLKtvhVmwU1sb4nM

Merkle Root

c0f48178cb2c03ac01764de0560fa41de7f9ebaf5b55c42eed649a3e2bdc4778
Transactions (1)
Coinbasec0f48178cb2c03…649a3e2bdc4778
1 in β†’ 1 out11.5500 XPM109 B
AFv3H3KX…wU1sb4nM
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.

5.935 Γ— 10¹⁰⁡(106-digit number)
59354235396044690966…74498635274506643079
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
5.935 Γ— 10¹⁰⁡(106-digit number)
59354235396044690966…74498635274506643079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.935 Γ— 10¹⁰⁡(106-digit number)
59354235396044690966…74498635274506643081
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
1.187 Γ— 10¹⁰⁢(107-digit number)
11870847079208938193…48997270549013286159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.187 Γ— 10¹⁰⁢(107-digit number)
11870847079208938193…48997270549013286161
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
2.374 Γ— 10¹⁰⁢(107-digit number)
23741694158417876386…97994541098026572319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.374 Γ— 10¹⁰⁢(107-digit number)
23741694158417876386…97994541098026572321
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
4.748 Γ— 10¹⁰⁢(107-digit number)
47483388316835752773…95989082196053144639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.748 Γ— 10¹⁰⁢(107-digit number)
47483388316835752773…95989082196053144641
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
9.496 Γ— 10¹⁰⁢(107-digit number)
94966776633671505546…91978164392106289279
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:57,609,075 XPMΒ·at block #6,795,625 Β· updates every 60s
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