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Block #139,034

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/28/2013, 6:26:38 PM Β· Difficulty 9.8294 Β· 6,663,392 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6fd69935bd0e3c61f583075439bf2cfde5f0d209412f2b2f00d5b5537e898f9f
View on Chainz β†—

Height

#139,034

Difficulty

9.829392

Transactions

2

Size

573 B

Version

2

Bits

09d45301

Nonce

150,639

Timestamp

8/28/2013, 6:26:38 PM

Confirmations

6,663,392

Mined by

⛏️ P2SHAL6pdaJviJYwucVGTtE6T3yxbZJM5cmDyB

Merkle Root

494f62bc868e5c259de9a738ba61e8d0fa173ecc120ec6dcf595b85c929db1cc
Transactions (2)
Coinbase95e9de530822f6…99fd517fbb6cad
1 in β†’ 1 out10.3400 XPM109 B
AL6pdaJv…JM5cmDyB
7b961e5f2c5dc1…852ebd1935abf3
2 in β†’ 2 out249.9700 XPM374 B
AMuxQ5WG…ZnnEiraGAKubZ5rY…L6ewHYWc
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.

5.511 Γ— 10⁹⁴(95-digit number)
55110507424575995816…81495572139464026779
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
5.511 Γ— 10⁹⁴(95-digit number)
55110507424575995816…81495572139464026779
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.511 Γ— 10⁹⁴(95-digit number)
55110507424575995816…81495572139464026781
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
1.102 Γ— 10⁹⁡(96-digit number)
11022101484915199163…62991144278928053559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.102 Γ— 10⁹⁡(96-digit number)
11022101484915199163…62991144278928053561
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
2.204 Γ— 10⁹⁡(96-digit number)
22044202969830398326…25982288557856107119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.204 Γ— 10⁹⁡(96-digit number)
22044202969830398326…25982288557856107121
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
4.408 Γ— 10⁹⁡(96-digit number)
44088405939660796653…51964577115712214239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.408 Γ— 10⁹⁡(96-digit number)
44088405939660796653…51964577115712214241
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
8.817 Γ— 10⁹⁡(96-digit number)
88176811879321593306…03929154231424428479
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:57,663,417 XPMΒ·at block #6,802,425 Β· updates every 60s
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