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Block #127,715

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/21/2013, 5:51:51 PM Β· Difficulty 9.7829 Β· 6,683,141 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8448ab4001142a173fcb87fc8f456fe4130ddffa10d7fbc65b2b0129e596d1ef
View on Chainz β†—

Height

#127,715

Difficulty

9.782949

Transactions

2

Size

1.25 KB

Version

2

Bits

09c86f60

Nonce

504,274

Timestamp

8/21/2013, 5:51:51 PM

Confirmations

6,683,141

Mined by

⛏️ P2SHANNP26d7MpgaTviL4gpx3seETjc8ABLJ7e

Merkle Root

0d288649c7c26830611500a1406730f8109f92f7dc280bf276beb74ef875a1b4
Transactions (2)
Coinbase3531a2ed8ac0de…7c826fa7d27bee
1 in β†’ 1 out10.4500 XPM109 B
ANNP26d7…c8ABLJ7e
3aefc8e4a5125d…e9a8979cdce637
7 in β†’ 1 out35.0875 XPM1.06 KB
AVbUYygu…86BSkU3f
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.

5.300 Γ— 10⁹⁢(97-digit number)
53009380987091372577…09879078156110408699
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
5.300 Γ— 10⁹⁢(97-digit number)
53009380987091372577…09879078156110408699
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.300 Γ— 10⁹⁢(97-digit number)
53009380987091372577…09879078156110408701
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
1.060 Γ— 10⁹⁷(98-digit number)
10601876197418274515…19758156312220817399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.060 Γ— 10⁹⁷(98-digit number)
10601876197418274515…19758156312220817401
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
2.120 Γ— 10⁹⁷(98-digit number)
21203752394836549031…39516312624441634799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.120 Γ— 10⁹⁷(98-digit number)
21203752394836549031…39516312624441634801
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
4.240 Γ— 10⁹⁷(98-digit number)
42407504789673098062…79032625248883269599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.240 Γ— 10⁹⁷(98-digit number)
42407504789673098062…79032625248883269601
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
8.481 Γ— 10⁹⁷(98-digit number)
84815009579346196124…58065250497766539199
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:57,730,943 XPMΒ·at block #6,810,855 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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