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Block #86,185

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/27/2013, 11:03:30 PM Β· Difficulty 9.2905 Β· 6,719,509 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dd6699a7f0ad4294423b6fe7686fe8dc5e737c4bebb4e2c41bc8796fff0fe198
View on Chainz β†—

Height

#86,185

Difficulty

9.290492

Transactions

1

Size

203 B

Version

2

Bits

094a5da9

Nonce

16,278

Timestamp

7/27/2013, 11:03:30 PM

Confirmations

6,719,509

Mined by

⛏️ P2SHAcuJraLTi7SA51dYsYdywtXJwqY66BS47Q

Merkle Root

3280ab188d0ff76d27713e74a6264df130ead1e9c888546b4a21ddcdd2b5d74f
Transactions (1)
Coinbase3280ab188d0ff7…21ddcdd2b5d74f
1 in β†’ 1 out11.5700 XPM109 B
AcuJraLT…Y66BS47Q
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.

2.997 Γ— 10¹⁰³(104-digit number)
29973418649399337592…67578235223215473839
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
2.997 Γ— 10¹⁰³(104-digit number)
29973418649399337592…67578235223215473839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.997 Γ— 10¹⁰³(104-digit number)
29973418649399337592…67578235223215473841
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
5.994 Γ— 10¹⁰³(104-digit number)
59946837298798675185…35156470446430947679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.994 Γ— 10¹⁰³(104-digit number)
59946837298798675185…35156470446430947681
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
1.198 Γ— 10¹⁰⁴(105-digit number)
11989367459759735037…70312940892861895359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.198 Γ— 10¹⁰⁴(105-digit number)
11989367459759735037…70312940892861895361
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
2.397 Γ— 10¹⁰⁴(105-digit number)
23978734919519470074…40625881785723790719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.397 Γ— 10¹⁰⁴(105-digit number)
23978734919519470074…40625881785723790721
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
4.795 Γ— 10¹⁰⁴(105-digit number)
47957469839038940148…81251763571447581439
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:57,689,634 XPMΒ·at block #6,805,693 Β· updates every 60s
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