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Block #155,164

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/8/2013, 3:47:32 AM Β· Difficulty 9.8654 Β· 6,647,477 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
de575e95741c205f6da90a22086ab2eb41eb646b62bd75ecb7a16efc669bd3e0
View on Chainz β†—

Height

#155,164

Difficulty

9.865354

Transactions

1

Size

198 B

Version

2

Bits

09dd87dd

Nonce

350,211

Timestamp

9/8/2013, 3:47:32 AM

Confirmations

6,647,477

Mined by

⛏️ P2SHAJn9y9WvUy9mvP3JMmTsGHrigbG4raUX4o

Merkle Root

8dc724e0117bac33bbd71619cdb0bbef34bbad477b2252c16b957aac290dad58
Transactions (1)
Coinbase8dc724e0117bac…957aac290dad58
1 in β†’ 1 out10.2600 XPM109 B
AJn9y9Wv…G4raUX4o
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.

2.833 Γ— 10⁹¹(92-digit number)
28336368182731975867…94631841208529663199
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
2.833 Γ— 10⁹¹(92-digit number)
28336368182731975867…94631841208529663199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.833 Γ— 10⁹¹(92-digit number)
28336368182731975867…94631841208529663201
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
5.667 Γ— 10⁹¹(92-digit number)
56672736365463951734…89263682417059326399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.667 Γ— 10⁹¹(92-digit number)
56672736365463951734…89263682417059326401
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
1.133 Γ— 10⁹²(93-digit number)
11334547273092790346…78527364834118652799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.133 Γ— 10⁹²(93-digit number)
11334547273092790346…78527364834118652801
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
2.266 Γ— 10⁹²(93-digit number)
22669094546185580693…57054729668237305599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.266 Γ— 10⁹²(93-digit number)
22669094546185580693…57054729668237305601
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
4.533 Γ— 10⁹²(93-digit number)
45338189092371161387…14109459336474611199
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:57,665,143 XPMΒ·at block #6,802,640 Β· updates every 60s
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